Question 216: Electromagnetic Induction

Question

A coil of resistance $400 \Omega$ is placed in ${ }^3$ magnetic field. If the magnetic flux ' $\phi$, ( Wb ) linked with the coil varies with time ' $t$ ' ( $s$ ) ${ }^{	ext {is }} \phi=50 \mathrm{t}^2+4$, the current in the coil at $\mathrm{t}=2 \mathrm{~s}$ will be

Accepted Answer

Step 1: FaradayÃ¢ÂÂs law of electromagnetic induction
The induced emf is:
$ e = -\frac{d\phi}{dt} $
Given: $\phi = 50t^2 + 4\ 	ext{Wb}$.
So,
$ \frac{d\phi}{dt} = \frac{d}{dt}(50t^2 + 4) = 100t $
At $t = 2\ 	ext{s}$:
$ \frac{d\phi}{dt} = 100(2) = 200\ 	ext{V} $
(The negative sign only tells about direction; for magnitude of current, take absolute value.)
Step 2: OhmÃ¢ÂÂs Law
The resistance of the coil is
$ R = 400\,\Omega $
So induced current is
$ I = \frac{e}{R} = \frac{200}{400} = 0.5\ 	ext{A} $
Ã¢ÂÂ Final Answer:
The current in the coil at $t = 2\ 	ext{s}$ is:
$ \boxed{0.5\ 	ext{A}} $
Correct Option: C

Answer

1 A

Answer

2 A

Answer

0.5 A

Answer

0.1 A

Electromagnetic Induction

A coil of resistance 400 \Omega is placed in { }^3 magnetic field. If the magnetic flux ' \phi, ( Wb ) linked with the coil varies with time ' t ' ( s ) { }^{\text {is }} \phi=50 \mathrm{t}^2+4, the current in the coil at \mathrm{t}=2 \mathrm{~s} will be

Choose the correct answer: